Processes of electron–positron plasma production by a high-energy neutrino in a strong magnetic field

Under the conditions of a strongly magnetized hyperaccretion disk around a Kerr black hole, we study the processes $\nu_i+\tilde\nu_i\to e^-+e^+$ and $\nu_i(\tilde\nu_i)\stackrel{B}{\longrightarrow} \nu_i(\tilde\nu_i)+e^++e^-$ of electron–positron plasma production near the disk. We calculate the plasma production rate in these processes for some known parameters of neutrino emission from the disk while the magnetic field distribution is determined by qualitative considerations. We show that the magnetic field influence on the cross section of the annihilation process $\nu_i+\tilde\nu_i\to e^-+e^+$ can be neglected if $\omega^2\gg eB\gg m_e^2$. We also show that the rate of energy–momentum production in the $e^+e^-$ plasma in the reaction $\nu_i(\tilde\nu_i)\stackrel{B}{\longrightarrow} \nu_i(\tilde\nu_i)+e^++e^-$ significantly depends on the magnetic field distribution over the disk. To obtain the final estimate of the plasma production rate in this reaction, the strong magnetic field distribution near the neutrino emitting part of the disk must be determined.